Earthquakes are considered one of the most catastrophic natural disasters due to its immense destructive potential, the extent of its effects and its sudden and unexpected occurrence, which can trigger serious consequences such as landslides, soil liquefaction, debris flow, etc. The study of seismic hazard is of great importance in geotechnical engineering, especially in cases involving special structures such as earth dams, under the socio-economic, environmental and security points of view. Seismic analysis of such special structures, even in areas of low seismicity as in Brazil, should be considered as a natural consequence of good design practice, since these facilities do need to remain safe and operational during their entire lifetime. The main motivation of this dissertation is to gather information and to present and discuss methods for the estimate of the seismic hazard and evaluation of the dynamic response of earth works. A tailings dam system located in Jamaica, within an area of high seismic activity, is analyzed in this dissertation, with the objective to establish the fundamental characteristics of the earthquake design from a probabilistic analysis of the regional seismic hazard. The slope stability of the dike and the permanent displacements caused by the earthquake are estimated by simple methods (pseudo-static stability method, Newmark method) and more complex solutions based on the finite element method.